Materials Characterization || Vibrational Spectroscopy for Molecular Analysis

9Vibrational Spectroscopyfor Molecular Analysis

Vibrational spectroscopy is a technique to analyze the structure of molecules by examin-ing the interaction between electromagnetic radiation and nuclear vibrations in molecules.Vibrational spectroscopy is significantly different from the spectroscopic methods usinginteractions between materials and X-rays introduced in Chapters 6 and 7. Vibrationalspectroscopy uses electromagnetic waves with much longer wavelengths, in the orderof 10−7 m, than the X-rays which are also electromagnetic waves but with wavelengthsin the order of 10−10 m. Typical electromagnetic waves in vibrational spectroscopy areinfrared light. Energies of infrared light match with vibrational energies of molecules. Vibra-tional spectroscopy detects the molecular vibrations by the absorption of infrared light or bythe inelastic scattering of light by a molecule. Vibrational spectroscopy can be used to examinegases, liquids and solids. It is widely used to examine both inorganic and organic materials.However, it cannot be used to examine metallic materials because they strongly reflect elec-tromagnetic waves. This chapter introduces two spectroscopic methods: Fourier transforminfrared spectroscopy (FTIR) and Raman microscopy (also called micro-Raman), which arethe vibrational spectroscopy techniques most commonly used by scientists and engineers formaterials characterization.

9.1 Theoretical Background

9.1.1 Electromagnetic Radiation

It is necessary to review electromagnetic radiation in general before discussing its interactionwith molecular vibrations. Electromagnetic radiation, traveling at a constant speed of light,varies in wavelength over 10 orders of magnitude and includes radio waves (∼102 m) toγ rays (∼10−12 m) as illustrated in Figure 9.1. Visible light occupies only a short range ofwavelengths (0.40–0.75 × 10−6 m). The energies of molecular vibrations match with thoseof electromagnetic radiation in a wavelength range near visible light. The electromagneticradiation in near visible light is able to change status of molecular vibrations and produce

Materials Characterization: Introduction to Microscopic and Spectroscopic Methods Yang Leng

© 2008 John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82298-2

254 Materials Characterization

Figure 9.1 Energy, frequency, wavelength and wavenumber ranges of electromagnetic waves. Fre-quency range of molecular vibrations is in infrared region close to visible light. (Reproduced from A.Fadini and F-M. Schnepel, Vibrational Spectroscopy: Methods and Applications, Ellis Horwood, Chich-ester, 1989.)

vibrational spectra of molecules. Vibrational spectroscopy characterizes the electromagneticwaves in terms of wavenumber (ν̄), which is defined as the reciprocal of wavelength in the unitof cm−1.

ν̄ = 1

λ(9.1)

Thus, the wavenumber is number of waves in a 1 cm-long wavetrain. It is convenient for us toremember that wavenumber is proportional to the frequency of the electromagnetic wave (ν)with a constant factor that is the reciprocal of the speed of light (c).

ν̄ = 1

cν (9.2)

The wavenumber represents radiation energy, as does wavelength. As we know, electromag-netic waves can be considered as photons. The photon energy is related to the photon frequency(νph).

E = hνph (9.3)

h is Planck’s constant (6.626 × 10−34 J s). Thus, the photon energy can be represented as itswavenumber.

E = hcv̄ (9.4)

The conversion constant (hc) is about 2.0 × 10−23 J cm s. For a wavenumber of 1000 cm−1,the corresponding energy should be only about 2.0 × 10−20 J or 0.12 eV. Note that this ismuch smaller than the photon energy of X-rays, which is in the order of 10,000 eV. As shown

Vibrational Spectroscopy for Molecular Analysis 255

in Figure 9.1, the vibrational spectra are in the wavenumber range from several hundreds tothousands. This indicates that the vibrational energy of molecules are only in the order of about10−2–10−1 eV.

9.1.2 Origin of Molecular Vibrations

Molecules in solids are always in vibration at their equilibrium positions, except at the temper-ature of absolute zero (−273.15 ◦C). Molecular vibrations can be simply modeled as masslesssprings connecting nuclei in a molecule. Figure 9.2 illustrates the simplest model of molecularvibrations: a diatomic molecule vibration by stretching or compressing the bond (a masslessspring) between two nuclei. The vibrational energy can be calculated using the spring model.The force (F) due to linear elastic deformation of the bond is proportional to displacement oftwo nuclei from its equilibrium distance re.

F = −K�r = −K(r − re) (9.5)

The force constant K is a measure of bond strength, and r is the distance between two nucleiafter displacement. Such vibration motion is considered as harmonic. The potential energy ofa harmonic vibration is expressed as Evib .

Evib = 1

2K(�r)2 = 1

2K(r − re)2 (9.6)

Figure 9.2 Diatomic model of molecular vibration. The centre of gravity does not change during thestretching vibration.


Figure 9.3 Potential energy (E) of diatomic molecule vibration. For a small displacement vibration(�r), the vibration motion can be treated as harmonic. Quantum theory divides the potential energy ofvibration into several levels as υ0, υ1, υ2, υ3, . . .

Figure 9.3 illustrates the potential energy of harmonic motion as a parabolic function ofdisplacement from the equilibrium position of nuclei. The harmonic curve differs from a realrelationship between energy and displacement in molecules. However, this harmonic assump-tion is a good approximation for molecular vibrations with small displacement. Although thepotential energy is a continuous function of the nuclear displacement, quantum mechanics tellus that the real vibrational energy of a molecule should be quantified. For harmonic vibration,the vibrational energy can be described.

Evib = hνvib

(υ + 1

2

)υ = 0, 1, 2, . . . (9.7)

υ is the vibrational quantum number, which defines distinguishable vibrational levels asshown in Figure 9.3 and νvib is the vibrational frequency of a molecule. The vibrationalfrequency of molecules is in the range of middle infrared (IR) frequencies (6 × 1012–1.2 × 1014 Hz). The ground state corresponds to υ = 0 with corresponding vibrationalenergy of 1

2hνvib; the first excited level (υ = 1) should have vibrational energy of 3

2hνvib; and

so on.Commonly, the vibrational spectroscopy covers a wavenumber range from 200 to

4000 cm−1. We should know that crystalline solids also generate lattice vibrations in addi-tion to molecular vibrations. The lattice vibrations refer to the vibrations of all the atomsin crystal lattice in a synchronized way. Such vibrations exhibit lower frequencies com-pared with those of common molecular vibrations and have a wavenumber range of about20–300 cm−1. Coupling between lattice and molecular vibrations can occur if the molecularvibrations lie in such a low wavenumber range. Molecular vibrations can be distinguishedfrom the lattice vibrations because they are not as sensitive to temperature change as latticevibrations.


9.1.3 Principles of Vibrational Spectroscopy

Infrared AbsorptionInfrared spectroscopy is based on the phenomenon of infrared absorption by molecular vibra-tions. When a molecule is irradiated by electromagnetic waves within the infrared frequencyrange, one particular frequency may match the vibrational frequency of the molecule (νvib).Consequently, the molecular vibration will be excited by waves with the frequency νph =νvib . The excitation means that the energy of molecular vibration will increase, normally by�υ = +1, as shown in Equation 9.7. In the meantime, the electromagnetic radiations withthe specific frequency νph will be absorbed by the molecule because the photon energy istransferred to excite molecular vibrations. The fundamental transition from υ = 0 to υ = 1dominates the infrared absorption, although other transitions may be possible.

Figure 9.4 illustrates an example of the HCl diatomic molecule with νvib = 8.67 × 1013 Hz.When it is excited by this frequency of electromagnetic radiation, the intensity of radiation atthat frequency (8.67 × 1013 Hz) will be reduced (absorbed) in the infrared spectrum while themolecule itself will be moved to a higher vibrational energy level. The absorption intensitydepends on how effectively the infrared photon energy can be transferred to the molecule. Theeffectiveness of infrared absorption is discussed in detail in Section 9.3 on Raman spectroscopy.Figure 9.5 shows an example of an infrared spectrum in which the intensity of transmittedinfrared radiation is plotted over a range of radiation wavenumbers. In the figure, an individualdeep valley represents a single vibration band that corresponds to a certain molecular vibrationfrequency.

Raman ScatteringRaman spectroscopy is based on the Raman scattering phenomenon of electromagneticradiation by molecules. When irradiating materials with electromagnetic radiation of singlefrequency, the light will be scattered by molecules both elastically and inelastically. Elas-tic scattering means that the scattered light has the same frequency as that of the radiation.Inelastic scattering means that the scattered light has a different frequency from that of theradiation. Elastic scattering is called Rayleigh scattering while inelastic scattering is calledRaman scattering.

Figure 9.4 Interaction between IR radiation and a HCl molecule. HCl stretching vibration with fre-quency = 8.67 × 1013 Hz absorbs the IR ray with the same frequency. (Reproduced with permission fromN.B. Colthup, L.H. Daly, and S.E. Wiberley, Introduction to Infrared and Raman Spectroscopy, 3rd ed.,Academic Press, San Diego. © 1990 Elsevier B.V.)


Figure 9.5 Typical IR absorption spectrum of hexanal. (Reproduced from P. Hendra, P.C. Jones, andG. Warnes, Fourier Transform Raman Spectroscopy: Instrumentation and Chemical Applications, EllisHorwood, Chichester, 1991.)

Both elastic and inelastic scattering can be understood in terms of energy transfer betweenphotons and molecules as illustrated in Figure 9.6. As mentioned before, photons of electromag-netic radiation can excite molecular vibration to a higher level when νph = νvib . If the excitedvibration returns to its initial level (Figure 9.6a), there is no net energy transfer from photons tomolecular vibration. Thus, the scattered photons from molecules will have the same frequencyas the incident radiation, similar to elastic collisions between photons and molecules. If the

Figure 9.6 Elastic and inelastic scattering of incident light by molecules. Rayleigh, elastic scattering;Stokes and anti-Stokes, inelastic scattering. (Reproduced from P. Hendra, P.C. Jones, and G. Warnes,Fourier Transform Raman Spectroscopy: Instrumentation and Chemical Applications, Ellis Horwood,Chichester, 1991.)


Figure 9.7 Typical Raman spectrum of polycrystalline graphite. (Reproduced with permission from G.Turrell and J. Corset, Raman Microscopy, Developments and Applications, Academic Press, HarcourtBrace & Company, London. © 1996 Elsevier B.V.)

excited molecular vibration does not return to its initial level, then scattered photons could haveeither lower energy or higher energy than the incident photons, similar to inelastic collisionbetween photons and molecules. Understandably, the energy change corresponds to the energydifference between initial and final levels of molecular vibration energy. The energy changes inscattered photons are expressed as their frequency changes. If the photon frequency decreasesfrom νph to (νph − νvib), the final energy level of molecular vibration is higher than the initialenergy (Figure 9.6b). This is called Stokes scattering. If the photon frequency increases fromνph to (νph + νvib), the final energy level is lower than the initial energy (Figure 9.6c). This iscalled anti-Stokes scattering. The intensity of anti-Stokes scattering is significantly lower thanthat of Stokes scattering. Thus, a Raman spectrum commonly records the frequency changescaused by the Stokes scattering by molecules. Such frequency change (difference between ra-diation and scattering frequency) is called the Raman shift in the spectrum, which should be inthe same range as the infrared absorption spectrum. Figure 9.7 shows an example of the Ramanspectrum in which the intensity of the Raman shift is plotted over a range of wavenumbers.An individual band of Raman shift corresponds to a molecular vibration frequency. Thus, bothinfrared and Raman spectra are plotted on the same scale of wavenumber.

9.1.4 Normal Mode of Molecular Vibrations

Understanding vibrational spectroscopy also requires basic knowledge of the vibrationalbehavior of molecules. The vibrations of nuclei in a molecule can be characterized with prop-erties of the normal mode vibration. The normal mode vibration of molecules has the followingcharacteristics:

� Nuclei in a molecule vibrate at the same frequency and in the same phase (passing theirequilibrium positions at the same time); and

� Nuclear motion does not cause rigid body movement (translation) or rotation of molecules.

The normal mode of molecular vibrations ensures that a molecule vibrates at its equi-librium position without shifting its center of gravity. Each type of molecule has a definednumber of vibration modes and each mode has its own frequency. We can examine the


Figure 9.8 Normal modes of vibrations in a CO2 molecule. (Reproduced from P. Hendra, P.C. Jones,and G. Warnes, Fourier Transform Raman Spectroscopy: Instrumentation and Chemical Applications,Ellis Horwood, Chichester, 1991.)

normal modes of molecular vibration by using simple molecule models. The simplest modelof molecular vibrations is the diatomic model, which has only one stretching mode as shownin Figure 9.2. For polyatomic molecules, the vibrations are more complicated. For example, alinear molecule of three atoms connected by two bonds has a total of four vibration modes asillustrated in Figure 9.8. These vibration modes include two stretching modes and two bend-ing modes. One stretching mode is symmetric (v1 in Figure 9.8) because the two bonds arestretched simultaneously. Another stretching mode is asymmetric (v3 in Figure 9.8) becauseone bond is stretched while the other is compressed. A bending mode changes the angle be-tween two bonds, but not the bond lengths. The two bending modes are notated as ν2 and ν4 inFigure 9.8. One is bending in the plane of the figure and the other is in the horizontal plane.

Two features of bending modes can be revealed from the molecule model in Figure 9.8.First, the bending vibration can occur in an infinite number of planes that are in neither thefigure plane nor the horizontal plane. However, we can ‘decompose’ any bending mode andexpress it in terms of v2 and v4, as for decomposing a vector. Second, the two bending modesin Figure 9.8 are indistinguishable in terms of frequency, because the relative movements ofnuclei in the two bending modes are physically identical. These two bending vibrations withthe same physical identity are the degenerate vibrations.

Normal vibration modes of a triatomic molecule with a bending angle are illustrated inFigure 9.9. There are three normal modes in this molecule: symmetric stretching, asymmetricstretching, and bending in the plane of the figure. Bending in the horizontal plane, similar toFigure 9.8, will generate rotation of the molecule, which is not considered as a vibration.

Number of Normal Vibration ModesIt is necessary for us to know how to count the number of normal vibration modes in a molecule.The total number of vibration modes relates to the degrees of freedom in molecular motion.For N atomic nuclei in a molecule, there are 3N degrees of freedom because each nucleuscan move in x, y or z directions in a three-dimensional space. Among the 3N degrees offreedom, however, there are three related to translation of a molecule along x, y or z direction


Figure 9.9 Normal modes of vibrations in a H2O molecule. (Reproduced from P. Hendra, P.C. Jones,and G. Warnes, Fourier Transform Raman Spectroscopy: Instrumentation and Chemical Applications,Ellis Horwood, Chichester, 1991.)

as a rigid body without stretching any bond connecting nuclei or changing any bond angle.Also, there are three degrees of freedom related to rotate a molecule around the x, y or z axesas a rigid body. The molecular vibrations are related only to internal degrees of freedom in amolecule without translation and rotation of the rigid body. Thus, the total vibration modes of anN-atomic molecule should be 3N − 6. For a linear molecule, the rotation around the bond axisis meaningless, considering the nuclei as points in space. Thus, there are only two rotationaldegrees of freedom for the molecule, and the total vibration modes should be 3N − 5 for alinear molecule. For example, the linear molecule of CO2 should have 9 − 5 = 4 vibrationmodes as shown in Figure 9.8.

Classification of Normal Vibration ModesIt is possible to categorize the various modes of molecular vibration modes into four types:

1. Stretching vibration (ν);2. In-planar bending vibration (δ);3. Out-of-planar bending vibration (γ); and4. Torsion vibration (τ).

Table 9.1 summarizes the features of the four vibration types. The last three types onlychange the bond angles, but do not stretch bonds. The torsion vibration can be considered asa special type of bending vibration as illustrated in Table 9.1. Thus, we can simply say thata vibration is either the stretching or the bending type. γ and τ only occur in molecules thathave at least three bonds. Generally, the vibration frequency varies with vibration type. Thefrequency decreases with increasing number of bonds involved. Special types of vibrationsmay occur in a larger molecule like in a polymer; however, they all can be derived from thesefour basic types.

9.1.5 Infrared and Raman Activity

Among the total number of normal vibration modes in a molecule, only some can be detectedby infrared spectroscopy. Such vibration modes are referred to as infrared active. Similarly, the


Table 9.1 Basic Types of Molecular Vibrations

(Data reproduced from A. Fadini and F-M. Schnepel, Vibrational Spectroscopy: Methods and Applications, EllisHorwood, Chichester, 1989.)

vibration modes that can be detected by Raman spectroscopy are referred to as Raman active.Consequently, only active modes can be seen as vibration bands in their respective infrared orRaman spectra. For example, Figure 9.10 shows the infrared and Raman spectra of chloroformmolecules. The infrared and Raman spectra complement each other as shown in Figure 9.10.The principles of infrared and Raman activity are complicated; thorough understanding requiresgroup theory of mathematics. Nevertheless, it is possible to understand the basic ideas withoutgroup theory as presented in the following sections.

Infrared ActivityTo be infrared active, a vibration mode must cause alternation of dipole moment in a molecule.A molecule has a center of positive charge and a center of negative charge. If these two centers

Figure 9.10 Comparison of IR and Raman spectrum with the example of CHCl3 molecules (Reproducedwith permission from N.B. Colthup, L.H. Daly, and S.E. Wiberley, Introduction to Infrared and RamanSpectroscopy, 3rd ed., Academic Press, San Diego. © 1990 Elsevier B.V.)


are separated by a distance (l), the dipole moment (µ) is defined.

µ = el (9.8)

e represents the amount of electrical charge at the charge center of the molecule. A moleculemay exhibit a permanent dipole moment with separated positive and negative centers, orzero dipole moment with superimposed centers. The infrared activity requires changes in themagnitude of normal vibration during the vibration. The magnitude is commonly representedwith a parameter q (which is equivalent to |�r| in Equation 9.5).

Mathematically, the requirement of infrared activity is expressed that the derivative of dipolemoment with respective to the vibration at the equilibrium position is not zero.

(∂µ

∂q

)q=0

�= 0 (9.9)

It does not matter whether the molecule has permanent dipole moment, because the dipolemoment can be induced by the electric field of an electromagnetic wave. For example, ifplotting the changes in dipole moment versus vibration modes of CO2 as in Figure 9.11a , wefind that vibration modes ν2, ν3, and ν4 are infrared active, but not ν1 (see Figure 9.8 for theCO2 vibration modes).

We can understand more about the infrared activity from Figure 9.12. The HCl molecule(Figure 9.12a) has a permanent dipole. Its stretching vibration is infrared active because thedipole distance changes during stretching vibration. The H2 molecule (Figure 9.12b) has acenter of symmetry and a zero dipole moment. It is infrared inactive, because the centersof positive and negative charge always remain as the center of symmetry and the dipolemoment is always equal to zero during vibration. The CO2 molecule also has a center ofsymmetry and zero dipole moment at equilibrium (Figure 9.12g). Its symmetric stretching isinfrared inactive, similar to the case of H2 (Figure 9.12c). However, its asymmetric stretching(Figure 9.12d) cannot retain the center of symmetry and change of dipole moment from 0 to

Figure 9.11 CO2 molecule vibrations: (a) dipole moment (µ) as a function of vibration displacement(q); and (b) polarizability (α) as a function of vibration displacement (q). (Reproduced from P. Hendra,P.C. Jones, and G. Warnes, Fourier Transform Raman Spectroscopy: Instrumentation and ChemicalApplications, Ellis Horwood, Chichester, 1991.)


Figure 9.12 Dipole moment changes during vibration of several molecules: (a) HCL stretching; (b) H2

stretching; (c) H2 center of symmetry; (d) CO2 asymmetric stretching; (e) CO2 bending; (f) CO2 sym-metric stretching; (g) CO2 center of symmetry; (h) CO3 asymmetric stretching; and (i) CO3 symmetricstretching. (Reproduced with permission from N.B. Colthup, L.H. Daly, and S.E. Wiberley, Introductionto Infrared and Raman Spectroscopy, 3rd ed., Academic Press, San Diego. © 1990 Elsevier B.V.)

a certain value. Similarly, the bending vibration (Figure 9.12e) also induces a non-zero dipolemoment during vibration. Thus, these two vibration modes are infrared active. The principleof vibration activity also applies to ion groups. For example, symmetric stretching of (CO3)2−(Figure 9.12i) is infrared inactive because the centers of negative charge from three negativelycharged oxygen ions always coincide with the center of positive charge from carbon. However,asymmetric stretching of (CO3)2− (Figure 9.12h) is infrared active. The bending vibrations of(CO3)2−, which are not shown in Figure 9.12, should also be infrared active.

Raman ActivityTo be Raman active, a vibration mode must cause polarizability changes in a molecule. Whena molecule is placed in an electric field, it generates an induced dipole because its posi-tively charged nuclei are attracted toward the negative pole of the field and its electrons areattracted toward the positive pole of the field. Polarizability (α) is a measure of the capa-bility of inducing a dipole moment (µ) by an electric field. It is defined in the followingequation.

µ = αE (9.10)

E is the strength of electric field. Polarizability determines the deformability of the electroncloud of a molecule by an external electric field, similar to the compliance of elastic defor-mation. Mathematically, Raman activity requires that the first derivative of polarizability with


respect to vibration at the equilibrium position is not zero.

(∂α

∂q

)q=0

�= 0 (9.11)

Again, using CO2 as the example, Figure 9.11b shows the change of α with respect to qand shows us that only v1 is Raman active because ∂α

∂qat q = 0 is not zero. Polarization of

molecules varies with directions in a three-dimensional space. For example, in a linear moleculesuch as CO2, the electron cloud has the shape of an elongated watermelon. Such an electroncloud is more deformable along its long axis than the directions perpendicular to the longaxis. The Raman activity can be illustrated using the changes of the polarizability ellipsoidthat represents the polarizability variation in three-dimensional space. The ellipsoid has thedimension of αi

−½ (the distance between the ellipsoid origin to ellipsoid surface in direction i)as shown in Figure 9.13 and Figure 9.14 . Generally, if the ellipsoid changes its size, shapeand orientation with vibration, that vibration is Raman active.

Figure 9.13 illustrates the change of the polarizability ellipsoid in normal mode vibrations ofthe H2O molecule. Its ν1, ν2 and ν3 modes are all Raman active because the ellipsoid changessize, shape or orientation as shown in Figure 9.13. We should interpret the ellipsoid change withcaution. Some modes with apparent ellipsoid change with vibrations are not Raman active.For example, the change of the polarizability ellipsoid in CO2 vibrations (Figure 9.14) doesnot mean Raman active in all modes. The symmetric stretching model, ν1, of CO2 is Ramanactive because the ellipsoid size changes during vibration. However, ν2 and ν3 of CO2 are

Figure 9.13 Normal modes of H2O vibrations and changes in polarizability ellipsoids. ν1, ν2 and ν3

are all Raman active. (Reproduced with permission from J.R. Ferraro, K. Nakamoto, and C.W. Brown,Introductory Raman Spectroscopy, 2nd ed., Academic Press, San Diego. © 2003 Elsevier B.V.)


Figure 9.14 Normal modes of CO2 vibrations and changes in polarizability ellipsoids. ν1 is Raman-active but ν3, ν2 and ν4 are not. (Reproduced with permission from J.R. Ferraro, K. Nakamoto, and C.W.Brown, Introductory Raman Spectroscopy, 2nd ed., Academic Press, San Diego. © 2003 Elsevier B.V.)

not Raman active, even though the ellipsoid changes during vibrations. The problem is thatellipsoid change is symmetric in +q and −q. Such displacement symmetry with respect to theequilibrium position makes the following expression zero.(

∂α

∂q

)q=0

= 0 (9.12)

Figure 9.11b clearly illustrates such a situation of ν2, ν3 and ν4. The example of acetylene mayfurther help our understanding. Figure 9.15 shows the two extreme positions of each vibration:1, 2, 3, 4, and 5 in the linear acetylene molecule (H C C H). The vibrations 1, 2 and 3 areRaman active, but not 4 and 5. In vibrations 1 and 2, the molecular shape is different in the twoextreme positions of vibrations. Thus, the polarizability ellipsoid will change its size or shape,similar to the ν1 mode of CO2. In vibration 3, the shape is identical at its two extreme positions,but there is an orientation change in its ellipsoid. The ellipsoid orientation change results fromthe clockwise and counterclockwise rotation of C C and C H bonds. In vibrations 4 and 5, thepolarizability ellipsoid does not change its size and shape because their two extreme positionsare identical. Vibration 5 does not cause the ellipsoid orientation to change either, because theclockwise rotation of one C H bond is compensated for by the counterclockwise rotation ofanother C H bond.

In summary, we can highlight the features of infrared- and Raman-active vibrations:

� A vibration can be one of three cases: infrared-active, Raman-active, or both infrared- andRaman-active; and

� In molecules that have a center of symmetry, infrared- and Raman-active vibrations aremutually exclusive.


Figure 9.15 Five normal modes of vibrations in acetylene H C C H (Reproduced with permissionfrom N.B. Colthup, L.H. Daly, and S.E. Wiberley, Introduction to Infrared and Raman Spectroscopy,3rd ed., Academic Press, San Diego. © 1990 Elsevier B.V.)

Further, it is helpful for us to know that vibrations of ionic bonds are strong in infraredspectroscopy (for example O H), and vibrations of covalent bonds are strong in Raman spec-troscopy (for example C C).

9.2 Fourier Transform Infrared Spectroscopy

Fourier transform infrared spectroscopy (FTIR) is the most widely used vibrational spectro-scopic technique. FTIR is an infrared spectroscopy in which the Fourier transform method isused to obtain an infrared spectrum in a whole range of wavenumbers simultaneously. It differsfrom the dispersive method, which entails creating a spectrum by collecting signals at eachwavenumber separately. Currently, FTIR has almost totally replaced the dispersive methodbecause FTIR has a much higher signal-to-noise ratio than that of dispersive method.

9.2.1 Working Principles

The key component in the FTIR system is the Michelson interferometer, as schematically illus-trated in Figure 9.16. The infrared radiation from a source enters the Michelson interferometer.The interferometer is composed of one beam-splitter and two mirrors. The beam-splitter trans-mits half of the infrared (IR) beam from the source and reflects the other half. The two splitbeams strike a fixed mirror and a moving mirror, respectively. After reflecting from the mirrors,the two split beams combine at the beam-splitter again in order to irradiate the sample beforethe beams are received by a detector.

The function of the moving mirror is to change the optical path lengths in order to generatelight interference between the two split beams. If the moving mirror is located at the samedistance from the beam splitter as the fixed mirror, the optical paths of the two split beams arethe same; thus, there is zero path difference. An optical path difference (δ) will be introduced bytranslating the moving mirror away from the beam-splitter. Changing the optical path differenceis similar to what happens in diffraction of crystallographic planes (Figure 2.6). The two splitbeams will show constructive and destructive interference periodically, with continuous changeof δ value. There will be completely constructive interference when δ = nλ, but completelydestructive interference when δ = ( 1

2 + n)λ A change of δ value is realized by a change in theposition of the moving mirror as illustrated in Figure 9.16.


Figure 9.16 Optical diagram of a Michelson interferometer in FTIR.

A plot of light interference intensity as function of optical path difference is called aninterferogram. Figure 9.17 illustrates interferograms of a radiation with two wavelengths λ

and 3λ. The interferogram at the top is the sum of interferograms of two light waves withwavelength λ and 3λ. The IR radiation from the FTIR source is composed of numerous wave-lengths. An interferogram of FTIR looks like that in Figure 9.18a. It has a sharp center burstthat dies off quickly into two wings. The center burst corresponds to the position of the movingmirror generating zero path difference at which the interferogram has the maximum intensitybecause all the waves have completely constructive interference (in phase). An interferogramirradiating the sample is the sum of sinusoidal waves with a range of wavelengths. The FTIRdetector receives interferogram signals which are transmitted to a sample (or reflected from asample). The interferogram received by the detector is not an infrared spectrum.

Figure 9.17 Interferograms: (a) sum of (b) and (c); (b) interferogram of light with wavelength 3λ; and (c)interferogram of light with wavelength λ. (Reproduced with permission from B.C. Smith, Fundamentalsof Fourier Transform Infrared Spectroscopy, CRC Press, Boca Raton. © 1996 CRC Press LLC.)


Figure 9.18 Plots of: (a) an interferogram; and (b) a Fourier transform from an interferogram to an IRspectrum. (Reproduced with permission from B.C. Smith, Fundamentals of Fourier Transform InfraredSpectroscopy, CRC Press, Boca Raton. © 1996 CRC Press LLC.)

Fourier transformation is necessary to convert an interferogram into an infrared spectrum,which is a plot of the light intensity versus wavenumber, as shown in Figure 9.18b. TheFourier transform is based on a fact that any mathematical function can be expressed as asum of sinusoidal waves. All the information of wave intensity as a function of wavelengthis included in the sum of sinusoidal waves. A computer equipped with FTIR constructs theinfrared spectrum using a fast Fourier transform (FFT) algorithm which substantially reducesthe computation time.

The Fourier transform as a mathematical tool has been mentioned in Chapter 3 when dis-cussing the relationship between real space and reciprocal space. Here it is emphasized as a toolwhich transfers information between a function in the time (t) domain and its correspondingone in the frequency (ω) domain.

F (ω) = 1√2�

∫ ∞

minus∞f (t)e−iωtdt (9.13)

In an FTIR instrument, the Fourier transform converts the intensity versus optical path differ-ence to the intensity versus wavenumber. The optical path difference can be considered to be inthe time domain because it is obtained by multiplying time with the speed of a moving mirror.The wavenumber can be considered in the frequency domain because it is equal to frequencydivided by the light speed.

9.2.2 Instrumentation

Infrared Light SourceThe infrared light source generates wideband radiation by heating solid materials to in-candescence using electric power. There are two commonly used IR sources: the Nernstglower, which is composed of mainly oxides of rare-earth elements; and the Globar, which is


Figure 9.19 Energy distributions of IR source with continuous wavelength radiation. Most IR sourcesare operated at a temperature where the energy maximum is near the short wavelength limit of IRspectrum. (Reproduced with permission from N.B. Colthup, L.H. Daly, and S.E. Wiberley, Introductionto Infrared and Raman Spectroscopy, 3rd ed., Academic Press, San Diego. © 1990 Elsevier B.V.)

composed of silicon carbide. The range of IR wavelength and energy distribution is highlytemperature sensitive as shown in Figure 9.19. Most IR sources are operated at the temper-ature where the maximum energy of radiation is near the short wavelength limit of the IRspectrum.

Beam-SplitterBeam-splitters should be made of material semi-transparent to infrared light. Beam-splittersshould reflect one half portion of infrared light to the moving mirror while transmitting therest infrared to a fixed mirror. The most common beam-splitter is a sandwich structure, with athin layer of germanium (Ge) between two pieces of potassium bromide (KBr); it works wellin the wavenumber range 4000–400 cm−1. Ge is able to split infrared light. KBr is a goodsubstrate material because it is transparent to infrared light, yet has good mechanical strength.It functions as a protective coating for the Ge. The drawback of using KBr as a substrate isits hygroscopic nature. KBr tends to absorb water vapor from the atmosphere and fog readilyforms on it. Thus, all FTIR instruments require low humidity or are sealed from atmosphere.The low humidity environment around the beam-splitter can be obtained by purging with dryair or nitrogen. More conveniently, the instrument is sealed such that the infrared beam passesthrough a window to reach the sample.

Infrared DetectorThe infrared detector is a device to measure the energy of infrared light from the samplebeing examined. It functions as a transducer to convert infrared light signals to electric signals.There are two main types: the thermal detector and the semiconductor detector. The keycomponent in a thermal detector is a pyroelectric crystal, of which the most commonly usedtype is deuterated triglycine sulfate (DTGS). Infrared radiation causes a temperature changein DTGS which, in turn, changes its dielectric constant. This dielectric constant affects its


capacitance and results in a voltage change across the DTGS. The DTGS detector operatesin the wavenumber range 4000–400 cm−1. It is simple and inexpensive but less sensitivethan the semiconductor detector. The most commonly used semiconductor detector is madeof mercury cadmium telluride (MCT). An MCT detector absorbs infrared photons which inturn causes the electrons to migrate from the valence band to the conduction band of thesemiconductor. The electrons in the conduction band generate electric current signals. TheMCT detector is up to 10 times more sensitive than the DTGS type; however, it detects anarrower band of radiation (4000–700 cm−1). The MCT detector needs to be cooled, commonlyto liquid nitrogen temperature (−196 ◦C), before operation. Another disadvantage of MCT isthat it saturates easily with high intensity radiation. This can be a problem for quantitativeanalysis.

9.2.3 Fourier Transform Infrared Spectra

An infrared spectrum converted from an interferogram by Fourier transform is called a singlebeam spectrum. A single beam spectrum includes both spectra from the sample and back-ground. The background spectrum contains only the information from the instrument andatmosphere, not from the sample being examined. The instrument contributions to backgroundspectrum are from the detector, beam-splitter, mirror and the IR source. The atmospheric con-tributions are mainly from water vapor and carbon dioxide. Figure 9.20 demonstrates how

Figure 9.20 (a) Single beam FTIR spectrum of background: a plot of raw detector response versuswavenumber without sample; (b) a sample single beam FTIR spectrum of polystyrene (vibrational bandsof polystyrene are superimposed on background spectrum); and (c) final FTIR spectrum of polystyrenethat only contains the vibration bands from the polystyrene sample (absorption intensity is expressed asthe transmittance). (Reproduced with permission from B.C. Smith, Fundamentals of Fourier TransformInfrared Spectroscopy, CRC Press, Boca Raton. © 1996 CRC Press LLC.)


Figure 9.20 (Continued)

significant background can make to the IR spectrum. Figure 9.20a shows a simple beamspectrum of a polystyrene sample. Figure 9.20b shows a single beam spectrum of the chamberwithout the polystyrene sample, which is a background spectrum. In the background spec-trum, typical water vapor bands at around 3500 and 1630 cm−1 and CO2 gas bands at 2350and 667 cm−1 are visible. To eliminate the background influence, the ratio of the single beamspectrum of a sample with the background spectrum should be made. This process results in atransmittance spectrum as shown in Figure 9.20c. Transmittance (T) is defined as the ratio ofintensities.

T = I/Io (9.14)


Figure 9.21 FTIR spectrum where the absorption intensity is expressed as absorbance. In this spectrumthe absorbance scale is normalized to a range 0–1. (Reproduced with permission from B.C. Smith,Fundamentals of Fourier Transform Infrared Spectroscopy, CRC Press, Boca Raton. © 1996 CRC PressLLC.)

I is the intensity measured in a single beam spectrum of sample and Io is the intensity measuredin the background spectrum. Transmittance is often expressed as %T, which forms the scale ofthe vertical axis in Figure 9.20c. The spectrum can also be presented as absorbance (A) versuswavenumber as shown in Figure 9.21. The absorbance is calculated from the transmittance.

A = −logT (9.15)

An FTIR spectrum is commonly expressed as a transmittance spectrum, in which vibration bandpeaks point downward. It can also be expressed as an absorbance spectrum, in which vibrationband peaks point upward (Figure 9.21). For quantitative analysis, an absorbance spectrumshould be used because the peaks of a transmittance spectrum are not linearly proportional toconcentration.

9.2.4 Examination Techniques

TransmittanceThe transmittance examination technique refers to the method of obtaining an infrared spectrumby passing an IR beam through a sample as illustrated in Figure 9.16. It is the most commonlyused examination method in FTIR for two reasons. First, the transmittance technique generateshigh signal-to-noise ratios, and second, it is suitable for samples in any of solid, liquid or gasphases. Its main disadvantage is the thickness limitation of samples. A thick sample will absorbso much of the infrared radiation that detecting infrared transmission becomes impossible.


Generally, for transmission examination, the sample thickness should not be more than 20 µm.On the other hand, a sample that is too thin (<1 µm) yields absorption bands too weak to bedetected.

Solid Sample PreparationSolid samples for transmittance examination can be in one of two forms: thin film or powder.Thin film samples are mainly polymeric materials. Casting films with polymer solutions isa commonly used method. Polymer films can also be made by mechanically pressing underelevated temperatures. Powder samples are made by grinding solid to powder and then dilutingthe powder with infrared-inert matrix materials. There are two typical methods for preparingpowder samples: making KBr pellets and making mulls. As mentioned in the instrumentationsection, KBr is transparent to infrared light. To make pellets, we grind a solid sample withKBr together to obtain powder particles with size less than 2 µm diameter. Then, the powdermixture is die-pressed to form a pellet. For the mull method, a solid sample is ground to apowder and then diluted with a mulling agent (usually mineral oil). The slurry of powder–oilis smeared on a KBr plate and sandwiched with another KBr plate. The mull method is simpleand inexpensive; however, the mulling agent contains long and straight chains of hydrocarbons,which absorb strongly around 3000 and 1400 cm−1, and hence it may complicate the samplespectrum.

Liquid and Gas Sample PreparationLiquid and gas samples do not need much preparation, but special cells to contain the samplesare often necessary. The simplest method to prepare a liquid sample is to make a capillary thinfilm of the liquid. The capillary thin film is made by placing a drop of liquid on a KBr plateand sandwiching it with another KBr plate. This method, however, is not suitable for volatileliquids. Liquid cells can be used for volatile liquid and toxic liquid samples, particularly forquantitative analysis. The spacing between the bottom and the top of liquid cell is typicallyfrom 1 to 100 µm. The cell is made of an infrared-transparent material. Typically, KBr is used;however, KBr should not be selected as the material for holding samples containing waterbecause water dissolves KBr. Instead, ZeSe or AgCl should be used because they are infrared-transparent but not water soluble. Cells for gas samples are structurally similar to cells forliquid but the dimension is much larger.

ReflectanceReflectance examination techniques refer to methods for obtaining an infrared spectrum byreflecting IR radiation from a solid or liquid sample. The main advantage is that bulk andcoating samples can be examined without destructive preparation. These techniques are espe-cially attractive for solid samples that are difficult to grind into powder and for fast sampleexamination. However, reflectance techniques are less popular than transmission because oftheir following disadvantages. First, infrared radiation has limited penetration into the sam-ple. A reflectance spectrum can only contain the infrared signals from the top 1 to 10 µmof a solid sample surface. This is a serious deficiency for a sample with possible chemicalcomposition change near its surface, and for quantitative analysis for which the exact pass-length of infrared light in the sample must be known. Second, it is more difficult to capturereflected infrared light than transmitted light. A reflectance spectrum will show much morenoise than the transmission spectrum for the same duration of examination. Third, reflectance


Figure 9.22 Reflectance types in FTIR spectroscopy.

techniques require special accessories, making the instrumentation more complicated andexpensive.

There are three types of reflectance techniques: specular, diffuse and reflection–absorptionas illustrated in Figure 9.22. Specular reflectance is applied to samples with smooth andpolished surfaces, diffuse reflectance is applied to samples with rough surfaces, andreflection–absorption is applied to IR-transparent thin films on IR opaque substrates. Thespecular and diffuse techniques are more widely used and are introduced in more detail in thefollowing text.

Specular reflectance occurs when an incident infrared beam strikes a smooth surface of a solidsample. The reflectance angle is the same as the incidence angle during specular reflectance.The optical arrangement of the specular reflectance accessory is schematically shown inFigure 9.23. It consists of two flat mirrors and a platform with a hole. The sample is placed overthe hole in the platform. The background spectrum is obtained by placing an ‘ideal reflector’of infrared light, such as a gold or aluminum mirror, over the hole. The optical arrangement isalso applied to a reflection–absorption case where there is reflectance on a smooth substratecoated with a thin film. In such case, the infrared beam goes through a double transmissionthrough the coating film. To obtain a background spectrum for examining the coating film, thesmooth surface of substrate material is placed over the platform hole.

Diffuse reflectance occurs when an incident infrared beam strikes a rough surface; the surfacecould be solid, powder or even liquid. The reflectance angle spreads over a wide range duringdiffuse reflectance. The optical arrangement of accessories for measuring diffuse reflectanceconsists of a focusing mirror, two flat mirrors and a sample cup as shown in Figure 9.24. Thefocusing mirror collects infrared light reflected off the sample. The sample cup can hold eitherpowder or liquid samples. Diffuse reflectance can be used to examine a sample of microgrammass. It can also be used to examine intractable objects such as a large piece of plastic. Another

Figure 9.23 Optical diagram of a simple specular reflectance accessory for FTIR instrument.


Figure 9.24 Optical diagram of a diffuse reflectance accessory for an FTIR instrument.

method for preparing samples for diffuse reflectance examination is to take a piece of abrasivepaper with silicon carbide particles and rub the surface of the object to be examined. Theabrasive paper will be covered with a certain amount of sample material. Then, we can placethe abrasive paper in the sample cup for FTIR examination.

9.2.5 Fourier Transform Infrared Microspectroscopy

FTIR spectroscopy can combine with microscopy for generating FTIR spectra from micro-scopic volumes in materials. The instrument for FTIR microspectroscopy is simply called theFTIR microscope, which is often attached to the conventional FTIR instrument. The FTIRmicroscope is increasingly used for materials characterization because of its simple opera-tion and FTIR spectra can be collected rapidly from microscopic volumes selected with themicroscope.

InstrumentationThe FTIR microscope has an optical system that can easily switch between visible lightobservation and infrared light spectroscopy. Also, the microscope can be operated in eithertransmittance or reflectance modes in order to meet the sample conditions, either transparentor opaque to light. The microscope has two light sources: a visible light source and infraredlight source. It also has an infrared detector and video camera or eyepieces, like a regular lightmicroscope. However, there is only one system of condenser and objective lens.

Figure 9.25 illustrates the optical paths of the microscope in the modes for FTIR spec-troscopy. Figure 9.25a shows the optical path of the infrared beam when the microscopeoperates in the transmittance mode, while Figure 9.25b shows the optical path in thereflectance mode. We should note that lenses used in FTIR differ from those used in con-ventional light microscope. The lenses used in FTIR microscopy are the Cassegrain type.The Cassegrain lens is composed of curved mirrors, not transparent glass pieces. Lightpassing the Cassegrain lens is reflected by a larger mirror with a parabolic shape and asmaller mirror with a hyperbolic shape for collection and focus of the beam, respectively. TheCassegrain lens is preferred for the reflecting lens in the FTIR microscope because it does notabsorb the energy of infrared light as a conventional optical lens does. The lens does not possess


Figure 9.25 Optical paths of FTIR microscope with IR radiation: (a) transmittance; and (b) reflectance.M, mirror; C, Cassegrain lens. (Reproduced by permission of PerkinElmer Inc.)


chromatic aberration either. The power of the Cassegrain objective used in FTIR is relativelow, usually less than 10×.

The selection of the microscopic area for FTIR microspectroscopy is achieved by a remoteaperture located between the objective and detector. The remote aperture commonly has arectangular opening with two pairs of knife-edged blades. The blades are often made from amaterial that is transparent to visible light but opaque to infrared light.

The infrared detector in the FTIR microscope must be highly efficient, such as the mercurycadmium telluride (MCT) detector. The IR radiation intensity from a microscopic area is sig-nificantly lower than from the sample in a conventional FTIR instrument. The MCT detectorcan ensure a sufficiently high signal-to-noise ratio for meaningful IR spectroscopy. The draw-back of using the MCT detector is the requirement of low temperature operation at −196 ◦C.It usually takes more than 8 hours to cool the MCT detector to the operating temperature usingliquid nitrogen.

ApplicationsIn principle, operation of the FTIR microspectroscopy is the same as for a conventional FTIRinstrument except the spectrum is obtained from a microscopic area or intensity distributionis mapped in the sample plane. A spectrum from an area in the order of 10 × 10 µm can beobtained. Mapping or FTIR imaging at micro-level resolution can be achieved by scanninga sample using a motorized sample stage. The resolution is primarily determined by the sizeof the focused IR beam and precision of motorized stage. Reflectance microspectroscopy ismore widely used than the transmittance mode in FTIR microscopy because minimal samplepreparation is required.

Figure 9.26 and Figure 9.27 illustrate an example of using the FTIR microscope to iden-tify a micro-sized particle. A contaminant particle is isolated, as shown in the micrograph(Figure 9.26). The twisted fiber is cotton. The particle attached to the fiber was examined withreflectance FTIR microspectroscopy. Figure 9.27 shows the IR spectrum of the particle and

Figure 9.26 Micrograph of isolated particulate contamination (AM) and cotton fiber (C). (Reproducedwith permission from H.J. Jumecki, Practical Guide to Infrared Microspectroscopy, Marcel Dekker,New York. © 1995 Taylor & Francis Group Ltd.)


Figure 9.27 IR spectrum of the isolated particle (lower) and IR spectrum of polystyrene (upper).(Reproduced with permission from H.J. Jumecki, Practical Guide to Infrared Microspectroscopy, MarcelDekker, New York. © 1995 Taylor & Francis Group Ltd.)

its identification as polystyrene by comparing the experimental spectrum with the standardpolystyrene spectrum.

9.3 Raman Microscopy

Raman microscopes are more commonly used for materials characterization than otherRaman instruments. Raman microscopes are able to examine microscopic areas of materi-als by focusing the laser beam down to the micrometer level without much sample preparationas long as a surface of the sample is free from contamination. This technique should be referredto as Raman microspectroscopy because Raman microscopy is not mainly used for imagingpurposes, similar to FTIR microspectroscopy. An important difference between Raman micro-and FTIR microspectroscopies is their spatial resolution. The spatial resolution of the Ramanmicroscope is at least one order of magnitude higher than the FTIR microscope.

Raman microspectroscopy (often called micro-Raman), like most Raman spectrometry, isof the dispersive type. It requires collecting a spectrum at each wavenumber separately, not likethe FTIR type that collects a spectrum in a range of wavenumbers simultaneously. Althoughthis chapter only describes the instrumentation for Raman microscopy, its working principlesand spectra are basically the same as those of conventional dispersive Raman instruments,which consist of the following elements:

� Laser source;� Sample illumination and collection system;� Spectral analyzer; and� Detection and computer control and processing system.


Figure 9.28 Optical diagram of a Raman microscope.

Raman spectroscopy requires highly monochromatic light, which can be provided only bya laser source. The laser source is commonly a continuous-wave laser, not a pulsed laser. Thelaser source generates laser beams with the wavelengths in the visible light range or close tothe range. In a Raman microscope, sample illumination and collection are accomplished inthe microscope. The microscope’s optical system enables us to obtain a Raman spectrum froma microscopic area: this is the main difference between the micro-Raman and conventionalRaman spectrometers.

9.3.1 Instrumentation

The optical arrangement of a Raman microscopic system is schematically illustrated inFigure 9.28. A laser beam passes through a filter to become a single wavelength beam, whichis then focused on a sample surface by the microscope. The Raman scattered light reflectedfrom a microscopic area of sample is collected by the microscope and sent to the detector.The Raman scattered light, which results from inelastic scattering, is weak compared withthe incident laser light. Thus, a holographic filter has to be used in order to block the laserlight entering the detector system. The wavelength of Raman scattering light is selected bya diffraction grating system before being recorded by a detector. More details of the opticalcomponents in a Raman microscopic system are presented below.

Laser SourceCommonly used laser sources are gas continuous-wave lasers such as Ar+, Kr+ andHe–Ne. Such laser sources are often capable of generating beams of multiple wavelengths. Forexample, Ar+ generates a range of wavelengths with different intensities. The highest intensitywavelengths include 515.4, 488.0 and 350.7 nm. Thus, it is necessary to filter out wavelengthsother than 515.4 nm when an Ar+ laser is used. The He Ne laser, however, generates beamsof only one wavelength at 632.8 nm. Gas laser sources generate several tens of mW of laserpower, but the laser power reaching the microscopic area of the sample is only about 5 mW.

Microscope SystemThe microscope in the Raman system is different from conventional microscopes used forobservation of microstructure in two aspects: the microscope only needs to illuminate a


Figure 9.29 Optical diagram of a Raman microscope. A pinhole spatial filter consists of a pinholeconfocal diaphragm (D1 and D2). (Reproduced with permission from G. Turrell and J. Corset, RamanMicroscopy, Developments and Applications, Academic Press, Harcourt Brace & Company, London. ©1996 Elsevier B.V.)

microscopic area, not the entire field, and the microscope must have a high numerical aperture(NA) in order to collect the Raman-scattered light over a large solid angle effectively. Theschematic layout in Figure 9.29 illustrates the optical features of the Raman microscope. Thebeam from the laser source is first filtered to obtain a monochromatic wavelength. Then, apinhole spatial filter removes the appearance of the diffraction rings and speckle noise fromaround the focused spot in order to obtain a clean point laser beam to illuminate the sample.This pinhole spatial filter (illustrated around pinhole D1 in Figure 9.29) is located at A inFigure 9.28. The clean laser beam is reflected by a beam-splitter and goes through an objectivelens to illuminate the sample.

The Raman-scattered light is collected by a wide-aperture objective lens and focused inan adjustable pinhole D2 placed in the image plane of the microscope. The second pinholespatial filter around D2 is located at B in Figure 9.28. The pinholes D1 and D2 are calledconfocal diaphragms because they are in exact optical conjugation positions with respect tothe point source in the object plane, similar to the confocal aperture in confocal microscopeintroduced in Chapter 1. This confocal arrangement ensures that only light originating from themicroscopic area of the sample is transmitted to the spectral analyzer and detector. These twopinhole spatial filters are important for illumination and Raman light collection. They multiplyand increase spatial resolution by eliminating stray light coming from the out-of-focus regionof the sample. By adjusting the pinhole diaphragm D2, the spatial resolution of the sample canreach 1 µm when a 100 × objective lens is used.

PrefiltersThe scattered light from the microscope must be passed through special filters before reachingthe spectral analyzer in order to remove elastically scattered light. The Raman light cannot


Figure 9.30 Spectral response of an ideal notch prefilter in micro-Raman spectroscopy to remove theelastically scattered light with wavenumber v̄o. (Reproduced with permission from G. Turrell and J.Corset, Raman Microscopy, Developments and Applications, Academic Press, Harcourt Brace & Com-pany, London. © 1996 Elsevier B.V.)

be seen without the filters, because the elastically scattered light has much higher intensitythan the inelastically scattered Raman light. The filter should ideally have a ‘notch’ feature, asshown in Figure 9.30. The notch is zero transmission in a narrow wavenumber range centeredon a exciting laser wavenumber. As illustrated in Figure 9.28 two holographic filters used inthe Raman microscope serve such a purpose.

Diffraction GratingThe key component of the spectral analyzer in the Raman microscope is the diffraction grating.It disperses Raman scattered light according to its wavenumbers. The surface of the diffractiongrating contains fine parallel grooves that are equally spaced as illustrated in Figure 9.31.When Raman scattered light is incident on the diffraction grating, the grating disperses thelight by diffracting it in a discrete direction. The light dispersion is based on Bragg’s Law

Figure 9.31 Principle of optical grating diffraction.


of diffraction angle and incident wavelength. The diffraction grating plays a role similar tothat of equal-spaced atomic planes in crystals. It diffracts the different wavelengths in discreteangles (Figure 9.31). One diffraction grating can cover a range of 1000 wavenumbers. For aRaman spectrum with a range of 400 to 4000 cm−1, in order to record the spectrum in thewhole range, the grating should change its angle with incident Raman scattered light. For amodern Raman microscope, the diffraction grating can continuously rotate with respect to theincident Raman scattered light and separate the Raman scattering wavenumbers smoothly. Thediffraction grating can provide spectral resolution of 1 cm−1.

Figure 9.31 illustrates the working principles of a diffraction grating. When light rays A andB are incident on the grooves of grating at angle I with respect to the grating substrate normal,they will be reflected by the grooved surfaces as reflected rays A′ and B′ at angle D with respectto the grating substrate normal. The path difference between A′ and B′ is calculated.

a sinI + a sin D

a is the distance between grooves. Constructive interference occurs when the following con-dition is satisfied.

a (sinI + sinD) = mλ (9.16)

m is an integer representing the order of diffraction. This basic grating equation is similar toBragg’s Law (Equation 2.3). Incident rays with different wavelengths are reflected at differentangles (are dispersed) according to the grating equation.

DetectorThe Raman scattered light separated according to wavelength is recorded by a detector which ismade from photoelectric materials. The detector converts photon signals to electric signals. Thedetector for Raman scattered light is often multi-channel and solid-state. The charged-coupleddevice (CCD) is the most commonly used detector. A CCD is a silicon-based semiconductorarranged as an array of photosensitive elements. A one-dimensional array of a CCD can detectand record light intensity of discrete wavelengths separated by the diffraction grating. TheRaman shift (mainly Stokes scattering) is calculated and plotted versus wavenumber in theRaman spectrum by computer processing.

9.3.2 Fluorescence Problem

Colored samples or impurities in polymer samples may absorb laser radiation and re-emit itas fluorescence. The intensity of fluorescence can be as much as 104 times higher than thatof Raman scattered light. The fluorescence problem is the major drawback of using Ramanspectroscopy. Thus, a Raman spectrum can be completely masked by fluorescence. Three mainmethods can be used to minimize fluorescence:

1. Irradiate the sample with high-power laser beams for a prolonged time to bleach out theimpurity fluorescence;

2. Change the wavelength of laser excitation to a longer wavelength (near infrared). The chanceof fluorescence is reduced because the excitation energy of the laser beam is lower; and


3. Use a pulsed laser source to discriminate against fluorescence because the lifetime of Ramanscattering (10−12–10−10 s) is much shorter than that of fluorescence (10−7–10−9 s). Thus,an electron gate can be used to preferentially measure the Raman signals.

Using a long-wavelength laser, however, generates a problem of Raman intensity reduction,because the light intensity decreases with wavelength exponentially. A Fourier transform typeof Raman spectroscopy (FT-Raman) has been developed that can solve fluorescence problems,particularly in conjunction with using a longer wavelength. FT-Raman uses a Nd–YAG lasersource, which generates excitation of IR wavelength (1064 nm) that does not cause fluores-cence in samples. Furthermore, the FT-Raman instrument collects the Raman signal using theMichelson interferometer, which can accommodate large beams. A larger beam can partiallycompensate for loss of using a longer wavelength. However, FT-Raman is not useful in Ramanmicroscopy in which the pinhole diaphragm has to be used to ensure spatial resolution.

9.3.3 Raman Imaging

Raman imaging is a technique to obtain spatial distribution of specific molecules in a sample.It is similar to element mapping in X-ray, electron and secondary ion mass spectroscopy. Theworking principle is to record the specific Raman peak that represents the specific componentin the sample, as schematically shown in Figure 9.32. Although it can be done with Ramanmicroscopy, Raman imaging is more difficult than other mapping techniques because theRaman scattered light is inherently weak.

Figure 9.32 Principle of Raman imaging. The spectra of A, B, C represent those of substrate, moleculeB and molecule C, respectively. (Reproduced with permission from G. Turrell and J. Corset, RamanMicroscopy, Developments and Applications, Academic Press, Harcourt Brace & Company, London. ©1996 Elsevier B.V.)


Raman imaging can be either obtained by a scanning or a direct-imaging method in theRaman microscope. The scanning method requires a scanning mechanism of focused laserbeam to generate a raster area in the sample, similar to scanning electron microscope (SEM)imaging. The scanning method is often not favorable because it is too time consuming. Unlikefor SEM imaging, the intensity of Raman scattered light is so low that dwell time of thelaser bean on each pixel should be long in order to obtain a satisfactory two-dimensionalimage.

The direct-imaging method is rather simple, obtaining a complete two dimensional imagefor a chosen wavenumber, which represents a molecule, by illuminating a whole area to beanalyzed. The entire sample can be done by defocusing the laser beam. Simple defocusingof the laser beam, however, will generate uneven distribution of laser intensity as a Gaussiandistribution with a maximum at the beam center and very low intensity near the beam edge.Special optical arrangement of the objective and condenser lenses in a Raman microscope canbe used to eliminate this problem.

A Raman image of specific molecule is obtained by mapping its unique wavenumber ofRaman scattering. Thus, only the scattered light with a wavenumber should be recorded bya two-dimensional detector. Raman wavenumber selection can be readily performed by thediffraction grating, which serves as a wavenumber filter. Good spatial resolution images of awhole illuminated area can be obtained by properly coupling the image plane of the objective tothe surface grating. A high quality Raman image also requires good spectral resolution (narrowrange of wavenumbers). To achieve both spatial and spectral resolution, more complicatedfiltering and optical systems are needed.

Figure 9.33 shows an example of Raman imaging with a direct-image method. The image ofthe epoxy film reveals the rubber particles in the epoxy matrix. The rubber exhibiting a Ramanscattering at 1665 cm−1 generates the image contrast. The rubber particles can effectivelyincrease the toughness of the epoxy.

9.3.4 Applications

Raman spectroscopy is attractive as an examination technique for ceramic and polymericmaterials because it can simply examine them by illuminating their surfaces regardless ofsample thickness and form. Raman microscopy is even more attractive because it can examinea microscopic area with diameters in the order of 1 µm. Raman microscopy is increasinglyused for materials characterization, including:

� Phase identification of polymorphic solids;� Polymer identification;� Composition determination;� Determination of residual strain; and� Determination of crystallographic orientation.

Phase IdentificationRaman microscopy is able to determine phases for polymorphic solids at the microscopiclevel. This is its advantage over conventional X-ray diffraction spectrometry in which thesample volume cannot be too small. Phase identification with Raman spectroscopy uses


Figure 9.33 Raman image of rubber particles in epoxy film at 1665 cm−1. (Reproduced with permissionfrom G. Turrell and J. Corset, Raman Microscopy, Developments and Applications, Academic Press,Harcourt Brace & Company, London. © 1996 Elsevier B.V.)

the characteristic vibration band(s) associated with a certain phase in a solid. For example,Table 9.2 lists characteristic vibration bands in Raman spectroscopy in several polymorphicsolids. This feature of Raman spectroscopy can be further demonstrated using carbon as an ex-ample. Figure 9.34 shows four types of carbon spectra which represent highly oriented graphite,polycrystalline graphite, amorphous carbon and diamond-like carbon. Significant differencesappear in Raman spectra for graphite and diamond because carbon atoms are bonded withsp2-type orbitals in graphite while they are bonded in sp3-type orbitals in diamond.

Polymer IdentificationRaman microscopy is able to identify the different type of polymers even though they all containC, H and O. For example, Figure 9.35 shows the Raman spectra of a laminated polymer film.Individual layers can be identified with Raman microscopy by focusing the laser beam on

Table 9.2 Phase Identification with Raman Microscopy

PolymorphicMaterials Phase 1 Bands (cm−1) Phase 2 Bands (cm−1)

Si3N4 α 262, 365, 514, 670, 850 β 185, 210, 230BN Cubic 1055 Hexagonal 1367ZrO2 Monoclinic 181, 192 Tetragonal 148, 264Carbon Diamond 1332 Graphite 1580


Figure 9.34 Characteristic spectra of carbon in different structures: (a) highly oriented graphite;(b) polycrystalline graphite; (c) amorphous carbon; and (d) diamond-like carbon. (Reproduced withpermission from G. Turrell and J. Corset, Raman Microscopy, Developments and Applications, Aca-demic Press, Harcourt Brace & Company, London. © 1996 Elsevier B.V.)

each of the layers in the cross-section of the laminated sample. The Raman spectra reveal thelaminated sample is composed of polyester, polyethylene and a layer of paper.

Raman spectroscopy is sensitive to polymer conformation. For example, a polymer blendof polybutadiene–polystyrene in which polybutadiene is used to increase toughness of thepolystyrene can be examined by Raman microscopy to identify its heterogeneity. Polybutadienehas three isomer conformations (cis-1,4, trans-1,4 and syndiotactic-1,2). These three types ofisomers can be identified from C C stretching modes as shown in Figure 9.36. The Ramanspectra of the copolymer indicate the difference in amounts of isomer types at the edge andthe center of the polybutadiene–polystyrene sample. Relative amounts of these isomer typesaffect the mechanical properties of the copolymer.

Composition DeterminationRaman microscopy has been used to monitor the amount of chemical elements present in,or added to, a solid. For example, Figure 9.37 shows that the graphite spectrum changesaccording to the number of molecules intercalated into its layered crystal structure. Molecularintercalation into gaps between crystal layers changes the bonding strength between the layers,which in turn changes the vibrational frequency in the graphite. The degrees of intercalation arerepresented by the stage number, which indicates intercalation occurs in every stage numberof layers; lower stage numbers mean higher degrees of intercalation. The graphite spectrum ishighly sensitive to the stage number of intercalated graphite as shown in Figure 9.37.

Raman microscopy has also been used to identify the composition variation of Si1−xGexsemiconductor materials. Figure 9.38 shows the Raman spectrum of a Si0.7Ge0.3 film on Sisubstrate. The vibrations of Si Si, Si Ge and Ge Ge bonding in the film generate three distinctRaman peaks. Note the Raman shift of Si Si vibration in Si1−xGex is different from that ofSi Si in pure Si. The composition variation of Si1−xGex is related to Raman peak positions inthe spectrum. Figure 9.39 shows that the Raman shift position is linearly related to the amountof Ge added in the Si.


Figure 9.35 Raman spectra of a laminated polymer film obtained with excitation of a 785-nm laser.(Reproduced from M.J. Pelletier, Analytical Applications of Raman Spectroscopy, Blackwell Science,Oxford. © 1999 Blackwell Publishing.)

Determination of Residual StrainResidual strain in a solid can also be determined by the shift of Raman bands because strainchanges the length of a bond between atoms and vibrational frequency is exponentially af-fected by the bond length. For example, compressive strain in a microscopic area of a samplewill reduce the bond length, and in turn, increase the corresponding vibrational frequency.Figure 9.39 clearly indicates the residual strain effect on Raman shift. A thin Si Ge film onSi substrate contains residual stress because the lattice parameter of Ge is different from thatof Si. The larger lattice parameter of Ge (0.566 nm) than that of Si (0.543 nm) generates biaxialcompression in the film. The residual compression strain alters the relationship between theRaman shift and Ge content as indicated by a solid line, compared with the dotted line thatrepresents the relationship when residual strain is not present in the Si-Ge film. In thicker films,


Figure 9.36 Raman spectra of polybutadiene–polystyrene copolymer in the C Cstretching regionshowing three distinct bands of polybutadiene isomers: cis-1,4 at 1650 cm−1, trans-1,4 at 1665 cm−1

and syndiotactic-1,2 at 1655 cm−1: (a) spectrum from the center of sample; and (b) spectrum from theedge of sample. (Reproduced with permission from G. Turrell and J. Corset, Raman Microscopy, De-velopments and Applications, Academic Press, Harcourt Brace & Company, London. © 1996 ElsevierB.V.)

the residual stress is relaxed by formation of cracks. Thus, the relation between Raman shiftand Ge content is closer to the dotted line.

Figure 9.40 shows another example of residual strain effects on the Raman spectrum. The Sistretching vibration changes its frequency when Si is in the form of a thin film on sapphire. Wecan compare the Raman band positions between the strain-free sample and strained sample toevaluate the bond length change, which can be converted to residual strain. The residual strainis commonly elastic in nature. Thus, the residual stress in materials can be determined withthe linear elastic relationship between strain and stress.

Determination of Crystallographic OrientationCrystallographic orientation in a sample area can also be determined by measuring the intensitychange of Raman scattered light in different polarization directions. The method of crystalorientation determination requires extensive theoretical treatment, which is beyond the scopeof this book. However, its concept can be understood from the following description. Whenpolarized light is scattered by a crystallographic plane of a sample, the polarization of lightwill be changed. The degree of change will depend on the angle between the polarizationdirection of incident light and direction of the crystallographic plane, and the angle betweenthe polarization direction of scattered light and direction of the crystallographic plane. If wemeasure the scattered light intensity change with polarization direction using an analyzer, thedirection of the crystallographic plane at the examined sample area can be determined.


Figure 9.37 Raman spectra of graphite and graphite intercalation compounds (GIC) with FeCl3. Alower stage number indicates a higher degree of intercalation.

9.4 Interpretation of Vibrational Spectra

Theoretical interpretation of molecular vibration spectra is not a simple task. It requires knowl-edge of symmetry and mathematical group theory to assign all the vibration bands in a spectrumprecisely. For applications of vibrational spectroscopy to materials characterization, we canstill interpret the vibrational spectra with relatively simple methods without extensive theoret-ical background knowledge. Here, we introduce some simple methods of vibrational spectruminterpretations.

9.4.1 Qualitative Methods

A simple way to qualitatively interpret vibrational spectra is the ‘fingerprint’ method of identi-fying materials. The fingerprint method includes spectrum comparison with a reference, andidentification of characteristic bands in spectra.


Figure 9.38 Raman spectrum of a Si1−xGex thin film with thickness of 121 nm on Si substrate, withargon laser (457.9 nm) excitation. (Reproduced from M.J. Pelletier, Analytical Applications of RamanSpectroscopy, Blackwell Science, Oxford. © 1999 Blackwell Publishing.)

Spectrum ComparisonSpectrum comparison is the simplest method to interpret a vibration spectrum. We do notneed to have much theoretical knowledge of spectrum interpretation for doing so. A samplecan be identified if its spectrum matches a reference in both band positions and intensities

Figure 9.39 Raman peak shift relationship with the composition change in Si1−xGex thin film. The plotalso indicates the film thickness effect on the relationship. (Reproduced from M.J. Pelletier, AnalyticalApplications of Raman Spectroscopy, Blackwell Science, Oxford. © 1999 Blackwell Publishing.)


Figure 9.40 Comparison of Raman peak position in bulk Si and an Si film on sapphire (SOS). (Repro-duced from M.J. Pelletier, Analytical Applications of Raman Spectroscopy, Blackwell Science, Oxford.© 1999 Blackwell Publishing.)

in the whole spectrum range. There is no need to assign vibration bands in a spectrum inspectrum comparison. Comparison of sample and reference spectra should satisfy the followingconditions; otherwise the spectra are not comparable:

� Both sample and reference spectra must be in the sample physical state (for example, eitherboth are liquid or solid); and

� Both sample and reference must be measured using the same techniques (for example, bothare dispersed with KBr for FTIR measurement).

Vibration frequencies in the solid phase are generally lower than in the liquid phase. Certainbands of solid samples do not appear in liquid and gaseous samples. Physical and/or chemicalinteractions of the sample with a dispersing matrix can alter the spectrum and make comparisonimpossible.

Typical applications of spectrum comparison include verifying whether synthetic materialsare identical to their natural counterparts, and determining the stability of materials over aperiod of time or in certain environments. For spectrum comparison, a region of spectrumbelow 1200 cm−1 is of importance, often called the ‘fingerprint region.’ The reason is thatthe region of relatively low wavenumber shows the vibrational bands involving large parts ofmolecules and crystals. The band positions and intensities in such a region are more sensitiveto minor chemical variations. For example, exchange of the A+ ion species in compoundsof AHMo5O16(H2O)H2Om, can be detected by comparing fingerprint regions in the Ramanspectra of the compounds as shown in Figure 9.41.


Figure 9.41 Comparison of Raman spectra of AHMo5O16(H2O)H2Om: A = (a) NH4+; (b) K+;

(c) Na+; and (d) compound spectrum in aqueous solutions. (Reproduced from A. Fadini and F-M.Schnepel, Vibrational Spectroscopy: Methods and Applications, Ellis Horwood, Chichester, 1989.)

Identifying Characteristic BandsVibrational frequencies of some atom groups are quite independent even if they are parts oflarger molecules and crystals. Such vibration bands serve as characteristic bands for atomgroups. A characteristic band for an atom group should satisfy the following conditions:

� The band occurs in all spectra of materials containing the atom group; and� The band is absent when materials do not contain the atom group.

For example, compounds containing the CH CH2 group exhibit a band near 1650 cm−1

in their IR spectra; compounds containing O H stretching vibration exhibit a band near3500 cm−1.

It is helpful to have basic knowledge of the relationship between vibrational frequencies andbond strength and atomic masses. We may use the relationship in understanding and assign-ing positions of characteristic bands in spectra. This relationship can be illustrated with thesimplest vibration of a diatomic model. Classical mechanics shows the vibrational frequencyrelationship.

νvib ∝√

f(m1 + m2)/(m1m2) (9.17)

f is the bond strength of atom 1 with mass m1 and atom 2 with mass m2. This equationindicates that vibrational frequency increases with the bond strength and decreases with atomicmass. Thus, it is understandable that the following relationships hold for vibration frequency


Figure 9.42 Positions of characteristic bands in vibrational spectra for some diatomic stretching vibra-tions. (Reproduced from A. Fadini and F-M. Schnepel, Vibrational Spectroscopy: Methods and Appli-cations, Ellis Horwood, Chichester, 1989.)

increases.

ν(C C) >ν(C C) > ν(C C) (9.18)

Also

ν(C H) > ν(C O) > ν(C Cl) (9.19)

Figure 9.42 illustrates approximate distributions of some diatomic stretching vibrationalbands in spectra. It clearly demonstrates the relationship between wavenumber (∝ νvib) andcharacteristics of bonds. Characteristic bands in Figure 9.42 show ranges instead of exactwavenumbers. This phenomenon reflects that the vibrational frequencies also depend on neigh-boring atoms in materials, even though the frequencies are mainly determined by bond strengthand atomic masses.

In general, the analysis method based on identifying characteristic bands is applicable topolymers and ceramics. Theoretically, vibrational spectra of such materials are generally com-plicated in nature. Their complex nature arises from several aspects: the presence of new bondscoupling repeated units, the large number of vibration bands (3N − 6) due to a large numberof atoms (N) in a polymer molecule, and vibration coupling of crystal lattices. Practically,vibration spectra of polymers and ceramics are often considered as a summation of the spectraof individual repeat units or functional groups, with slight modifications due to the presenceof new bond coupling between the repeated units. The characteristic bands can still be identi-fied; however, the bands may be broadened or slightly shifted. Relatively few extra vibrationbands from molecular chain and crystal structures are observed in spectra of polymers andceramics.


Figure 9.43 Raman spectra of plasma sprayed calcium phosphate coating shows the difference inhydroxyapatite content by comparing intensity of the OH stretching band at: (a) near substrate; (b) inthe middle; and (c) near the surface of the coating layer.

We may use the characteristic bands to distinguish compounds that include or are composedof similar ion groups. For example, hydroxyapatite [Ca5(PO4)3OH] can be distinguished fromother compounds of calcium phosphates, for example tricalcium phosphate [Ca3(PO4)2], inRaman spectroscopy by its hydroxyl group. Raman microscopy (Figure 9.43) demonstratesthat a calcium phosphate coating layer produced by plasma sprayed on a titanium substrateexhibits compositional change in the coating layer. The relative amount of hydroxyapatite indifferent depths of the coating layer of calcium phosphate can be estimated by comparing theintensity of O H stretching band at about 3600 cm−1 in different locations of a coating layer:near the surface, in the middle of layer and close to substrate interface.

On the other hand, limitations of using characteristic bands should not be ignored. For ex-ample, some characteristic bands may overlap each other. The vibrational bands for O H andN H stretching occur in the same region in the spectra, as shown in Figure 9.42. Also, certainfactors can shift or eliminate characteristic bands. Commonly, characteristic bands are distinctfor organic materials, but may not be for inorganic materials. One reason is strong vibra-tional coupling in inorganic materials. Such coupling occurs when bond strength and atomicmasses vary slightly through inorganic molecules. For example, an isolated C O stretchingband is located at 1620–1830 cm−1. For CO2 with two C O bonds sharing one carbon atom,the stretching vibrations of C O become one symmetric and one anti-symmetric vibration(Figure 9.8). The two distinctive vibrational bands are located at 1345 cm−1 and 2349 cm−1,respectively.

Band IntensitiesInterpreting the intensities of vibrational bands in a vibrational spectrum is not straightforward.The band intensity is not simply proportional to the number of atoms involved with suchspecific vibration. The intensity varies with types of bonds and types of spectroscopy, eitherIR or Raman. The intensity of an IR absorption band is proportional to the square of its change


in dipole moment during vibration.

I(IR) ∝(

∂µ

∂q

)2

(9.20)

But the intensity of a Raman shift is proportional to the square of its change in polarizabilityduring vibration.

I(Raman) ∝(

∂α

∂q

)2

(9.21)

Table 9.3 Intensity Estimations of IR and Raman Bands for Certain Structure Elements


Figure 9.44 Comparison of IR and Raman spectra of copolymer ethylene–vinyl acetate (EVA). EVAis distinguished by the C Cbands. (Reproduced from M.J. Pelletier, Analytical Applications of RamanSpectroscopy, Blackwell Science, Oxford. © 1999 Blackwell Publishing.)

In practice, some simple rules are useful to estimate the band intensities:

� Polar bonds yield intense IR but weak Raman bands;� Weak polar or non-polar bonds yield intense Raman but weak IR bands; and� Intensity increases with number of identical structural elements in a molecule.

To illustrate, Table 9.3 lists several structural elements of molecules and their intensity inIR and Raman bands. The intensity of a vibration band is often more complicated than isindicated in this table. For example, Table 9.3 suggests that unsaturated bonds ( and )exhibit higher band intensities in Raman than in IR spectra. However, this is not always true.For example, Figure 9.44 shows a comparison of IR and Raman spectra of a copolymer sample,EVA (ethylene–vinyl acetate). The C O band shows high intensity in the IR spectrum, not theRaman spectrum. More detailed information about band intensities, including band contoursand effects of vibration symmetry on intensity, can be found in the references listed at the endof this chapter.

9.4.2 Quantitative MethodsQuantitative Analysis of Infrared SpectraThe concentration of certain components in a multi-component sample can be determinedby quantitative analysis of its vibrational spectrum. Similar to quantitative analysis of X-raydiffraction spectra, the concentration of a component can be evaluated from the intensitiesof its vibration bands. For an IR spectrum, concentration is proportional to absorbance (A)according to the absorption law, also called Beer’s Law.

A = −logT = logIo

I= alC (9.22)


Figure 9.45 Baseline method for determining absorbance. (Reproduced with permission from N.B.Colthup, L.H. Daly, and S.E. Wiberley, Introduction to Infrared and Raman Spectroscopy, 3rd ed.,Academic Press, San Diego. © 1990 Elsevier B.V.)

a is the absorptivity that is a constant at a particular wavenumber, and l is the sample thicknessor the path length of radiation in the sample. I and Io are defined in Equation 9.14. Theconcentration (C) can be determined by measuring the magnitude of absorbance from anIR spectrum, if a and l are known. These latter two parameters can be obtained by using acalibration graph of A versus C if we have several samples of known concentrations.

The absorbance A is commonly obtained by peak height measurement in quantitative IRanalysis. Figure 9.45 illustrates how to measure I and Io from a conventional IR spectrum inwhich %T is plotted against the wavenumber. We should note that the transmittance (T), cannotbe directly used for quantitative analysis. The figure shows a popular method for measuringIo using a baseline method. The baseline is drawn tangentially to the spectrum at the wings ofthe analytical band. The baseline intersection with a vertical line at the wavenumber of bandpeak is used as Io.

We should know that the peak height is sensitive to instrument resolution. The peak areameasurement under a vibration band shows much less instrumentation dependence. The peakarea represents the integrated intensity of the vibration band and is proportional to the squareof the change in dipole moment with respect to the normal coordinate as Equation 9.20.

For analysis of two-component materials, a ratio method can be used for quantitative analysisbased on Beer’s Law. For example, there is a mixture of two components and two componentshave their own characteristic bands, which do not interfere with each other. Then, the ratio oftheir absorbance will be calculated.

A1

A2= a1l1C1

a2l2C2(9.23)

The path lengths should be the same in the same sample. We can determine the ratio of a1:a2using a standard sample in which C1 is known.

a1

a2=

(1

C1− 1

)A1

A2(9.24)


For analysis of multi-component materials with overlapping vibration bands, Beer’s Law canstill be used because absorbances of components are additive. Combining a and l as a singleparameter k, the absorbance of components is expressed.

A = k1C1 + k2C2 + k3C3 + . . . knCn (9.25)

There will be n number of equations and n × n number of k parameters for a sample with nnumber of components. For example, a three-component system should have the followingexpressions.

A1 = k11C1 + k12C2 + k13C3

A2 = k21C1 + k22C2 + k23C3

A3 = k31C1 + k32C2 + k33C3

(9.26)

The best way to write a group of linear equations like Equation 9.26 is to use the matrix form.

A = KC (9.27)

The concentrations of components should be resolved as C.

C = PA (9.28)

where P = K−1, the inverse of K matrix. This method is required to determine all the k valuesin the K matrix for standard samples.

Quantitative Analysis of Raman SpectraRaman spectroscopy is a scattering, not an absorption technique as FTIR. Thus, the ratiomethod cannot be used to determine the amount of light scattered unless an internal stan-dard method is adopted. The internal standard method requires adding a known amount ofa known component to each unknown sample. This known component should be chemicallystable, not interact with other components in the sample and also have a unique peak. Plottingthe Raman intensity of known component peaks versus known concentration in the sample,the proportional factor of Raman intensity to concentration can be identified as the slope of theplot. For the same experimental conditions, this proportional factor is used to determine theconcentration of an unknown component from its unique peak. Determining relative contentsof Si and Ge in Si Ge thin films (Figure 9.38 and Figure 9.39) is an example of quantitativeanalysis of a Raman spectrum.

References

[1] Fadini, A. and Schnepel, F-M. (1989) Vibrational Spectroscopy, Methods and Applications, Ellis Horwood,Chichester.

[2] Smith, B.C. (1996) Fundamentals of Fourier Transform Infrared Spectroscopy, CRC Press, Boca Raton.[3] Ferraro, J.R., Nakamoto, K. and Brown, C.W. (2003) Introductory Raman Spectroscopy, 2nd edition, Academic

Press, San Diego.


[4] Turrell, G. and Corset, J. (1996) Raman Microscopy, Developments and Applications, Academic Press, HarcourtBrace & Company, London.

[5] Hendra, P., Jones, P.C. and Warnes, G. (1991) Fourier Transform Raman Spectroscopy, Instrumentation andChemical Applications, Ellis Horwood, Chichester.

[6] Colthup, N.B., Daly, L.H. and Wiberley, S.E. (1990) Introduction to Infrared and Raman Spectroscopy, 3rdedition, Academic Press, San Diego.

[7] Nakamoto, K. (1986) Infrared and Raman Spectra of Inorganic and Coordination Compounds, John Wiley &Sons, New York.

[8] Mohan, J. (2000) Organic Spectroscopy, Principles and Applications, CRC Press, Boca Raton.[9] Chase, D.B. and Rabolt, J.F. (1994) Fourier Transform Raman Spectroscopy, From Concept to Experiment,

Academic Press, San Diego.[10] Pelletier, M.J. (1999) Analytical Applications of Raman Spectroscopy, Blackwell Science, Oxford.[11] Jumecki, H.J. (1995) Practical Guide to Infrared Microspectroscopy, Marcel Dekker, New York.

Questions

9.1 Can we identify atoms or monatomic ions of materials using vibrational spectroscopy?Why?

9.2 Determine the normal modes of planar molecule XY3 with a central symmetric configu-ration, where X is located at the center of the molecule.

9.3 Find out the normal modes of tetragonal molecule XY4.9.4 List the similarities of, and differences between, IR and Raman spectroscopy in terms of

working principles, spectra and detectable vibration bands.9.5 What is/are the advantage(s) of using an FTIR instead of dispersive IR spectrometer?9.6 Why does transmission IR require samples to have thickness in the range 1–20 µm? How

can we examine materials in bulk form?9.7 Why does IR spectroscopy require radiation containing continuous wavelengths while

Raman spectroscopy requires a monochromatic source?9.8 What are the special requirements for a microscope in a Raman microscope compared

with a conventional light microscope?9.9 Where is the ‘fingerprint region’ in a vibration spectrum?9.10 What kinds of vibrational bands are considered as characteristic bands?

Materials Characterization || Vibrational Spectroscopy for Molecular Analysis

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